We investigate the magnetization reversal of single-domain magnetic nanoparticle driven by linear down-chirp microwave magnetic field pulse. Numerical simulations based on the Landau-Lifshitz-Gilbert equation reveal that solely down-chirp pulse is capable of inducing subnanosecond magnetization reversal. With certain range of initial frequency and chirp rate, the field amplitude required is much smaller than that of constant frequency microwave field. The fast reversal is because the down-chirp microwave field acts as energy source and sink for the magnetic particle before and after crossing over the energy barrier respectively. Applying a spin-polarized current additively to the system further reduces the microwave field amplitude. Our findings provide a new way to realize low-cost and fast magnetization reversal.